Abstract
Abstract In the ΛCDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second‐order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second‐order scalar, vector, and tensor metric corrections are suitable at arbitrary distances, including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfillment of all Einstein equations, as well as self‐consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological back-reaction manifestations by means of relativistic simulations are also outlined.
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